U.S. patent number 7,330,801 [Application Number 11/461,094] was granted by the patent office on 2008-02-12 for signal separation using rank deficient matrices.
This patent grant is currently assigned to Interdigital Technology Corporation. Invention is credited to Steven J. Goldberg, Yogendra Shah.
United States Patent |
7,330,801 |
Goldberg , et al. |
February 12, 2008 |
**Please see images for:
( Certificate of Correction ) ** |
Signal separation using rank deficient matrices
Abstract
A communications device includes an antenna array for receiving
different summations of source signals from a plurality of signal
sources, a receiver coupled to the antenna array for receiving the
different summations of source signals, and a signal separation
processor coupled to the receiver. Processing by the signal
separation processor includes creating a matrix based upon the
different summations of source signals, with the matrix being
defined by linear independent equations with fewer equations than
unknowns. The matrix is underdetermined, and parameters associated
with the matrix are modified based upon different sets of parameter
values, and respective matrix quality factors associated with the
different sets of parameter values are determined. The matrix is
then biased with a preferred set of parameter values so that the
solution space may be narrowed for obtaining a solution.
Inventors: |
Goldberg; Steven J.
(Downingtown, PA), Shah; Yogendra (Exton, PA) |
Assignee: |
Interdigital Technology
Corporation (Wilimington, DE)
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Family
ID: |
37693753 |
Appl.
No.: |
11/461,094 |
Filed: |
July 31, 2006 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20070024502 A1 |
Feb 1, 2007 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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60703609 |
Jul 29, 2005 |
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Current U.S.
Class: |
702/85; 342/383;
702/196 |
Current CPC
Class: |
G01S
3/74 (20130101) |
Current International
Class: |
G06F
19/00 (20060101); G01S 3/16 (20060101); G06F
15/00 (20060101) |
Field of
Search: |
;702/85,190-197
;342/350,367,378,380-384 ;375/148 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Li et al., Blind Separation of Linear Mixtures of Digital Signals
Using Successive Interference Cancellation Iterative Least Squares,
1999 IEEE, pp. 2703-2706. cited by examiner .
Yao et al., Blind Detection of Synchronous CDMA in Non-Gaussian
Channels, Jan. 2004, IEEE Transactions on Signal Processing, vol.
52, No. 1, pp. 271-279. cited by examiner .
Yao et al., On Regularity and Identifiability of Blind Source
Separation Under Constant-Modulus Constraints, Apr. 2005, IEEE
Transactions on Signal Processing, vol. 53, No. 4, pp. 1272-1281.
cited by examiner .
Donoho et al., The Simplest Solution to an Underdetermined system
of Linear Equations, ISIT 2006, Seattle, USA, Jul. 9-14, 2006.
cited by other .
Donoho, For Most Large Underdetermined Systems of Linear Equations
the Minimal .lamda..sup.1-norm Solution is Also the Sparsest
Solution, Sep. 16, 2004. cited by other.
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Primary Examiner: Barlow; John
Assistant Examiner: Le; Toan M.
Attorney, Agent or Firm: Allen, Dyer, Doppelt, Milbrath
& Gilchrist, P.A.
Parent Case Text
RELATED APPLICATION
This application claims the benefit of U.S. Provisional Application
Ser. No. 60/703,609 filed Jul. 29, 2005, the entire contents of
which are incorporated herein by reference.
Claims
That which is claimed is:
1. A communications device comprising: an antenna array for
receiving different summations of source signals from a plurality
of signal sources; a receiver coupled to said antenna array for
receiving the different summations of source signals; and a signal
separation processor coupled to said receiver for creating a matrix
based upon the different summations of source signals, the matrix
being defined by linear independent equations with fewer equations
than unknowns, separating from the matrix a desired source signal
from the plurality of source signals, determining an error rate
associated with the desired source signal, and comparing the error
rate to a threshold, if the error rate is not acceptable based upon
the comparing, then modifying parameters associated with the matrix
based upon a first set of parameter values and based upon at least
one second set of parameter values, determining respective matrix
quality factors associated with the first set of parameter values
and with the at least one second set of parameter values, comparing
the respective matrix quality factors for determining a preferred
set of parameter values, and biasing the matrix with the preferred
set of parameter values.
2. A communications device according to claim 1 further comprising
separating from the biased matrix the desired source signal from
the plurality of source signals.
3. A communications device according to claim 1 further comprising
repeating for the biased matrix the separating, determining of the
error rate and the comparing thereof, the modifying, determining of
the respective matrix quality factors, the comparing for
determining a new preferred set of parameter values, and biasing of
the biased matrix with the new preferred set of parameter
values.
4. A communications device according to claim 1 wherein the
parameters associated with the matrix are modified so that the
respective matrix quality factors are based upon error rates
associated with the first set of parameter values and the at least
one second set of parameter values.
5. A communications device according to claim 1 wherein the
parameters associated with the matrix are modified so that the
respective matrix quality factors are based upon constellation
clouds associated with the first set of parameter values and the at
least one second set of parameter values.
6. A communications device according to claim 1 wherein the
parameters associated with the matrix are modified so that the
respective matrix quality factors are based upon determined lengths
of Viterbi paths associated with the first set of parameter values
and the at least one second set of parameter values.
7. A communications device according to claim 1 wherein each set of
parameter values associated with the matrix corresponds to a range
interval of solutions of the matrix.
8. A communications device according to claim 7 wherein at least a
portion of the range intervals of solutions overlap.
9. A communications device according to claim 1 wherein the linear
independent equations include channel coefficients; and wherein
each set of parameter values associated with the matrix corresponds
to a range interval of the channel coefficients.
10. A communications device according to claim 1 wherein creating
the matrix includes determining a power level of the different
summations of source signals; and wherein each set of parameter
values associated with the matrix corresponds to a range interval
of the power levels.
11. A communications device according to claim 1 wherein separating
from the matrix the desired source signal from the plurality of
source signals is based upon at least one of a Kolmogorov
complexity minimization and a convex optimization.
12. A communications device according to claim 1 wherein the error
rate is compared to a threshold for determining acceptability.
13. A communications device according to claim 1 wherein after
determining the error rate and before determining the respective
matrix quality factors; further comprising adding entries to the
matrix so that a number of the unknowns in the matrix is
reduced.
14. A communications device according to claim 13 wherein the
entries are added based upon at least one of adjusting range
intervals of the matrix, adjusting relationships between entries,
and adjusting power levels of the matrix entries.
15. A communications device according to claim 1 wherein said
antenna array comprises at least one antenna element.
16. A communications device according to claim 15 wherein said at
least one antenna element comprises a plurality of active antenna
elements so that said antenna array forms a phased array.
17. A communications device according to claim 15 wherein said at
least one antenna element comprises a plurality of active antenna
elements so that said antenna array forms a switched beam
antenna.
18. A communications device according to claim 1 wherein said
antenna array comprises a ground plane adjacent said at least one
antenna element; and wherein said at least one antenna element
comprises an active antenna element; at least one passive antenna
elements comprising an upper half and a corresponding lower half,
and a variable reactive load connecting said upper half to said
ground plane for changing an antenna pattern.
19. A communications device according to claim 1 wherein said
antenna array comprises a ground plane adjacent said at least one
antenna element; and further comprising a controller coupled to
said ground plane for changing an antenna pattern.
20. A method for operating a communications device comprising:
receiving at the antenna array different summations of source
signals from a plurality of signal sources; providing the different
summations of source signals to the receiver; and processing by the
signal separation processor the different summations of the source
signals received by the receiver, the processing comprising
creating a matrix based upon the different summations of source
signals, the matrix being defined by linear independent equations
with fewer equations than unknowns, separating from the matrix a
desired source signal from the plurality of source signals,
determining an error rate associated with the desired source
signal, and comparing the error rate to a threshold, if the error
rate is not acceptable based upon the comparing, then modifying
parameters associated with the matrix based upon a first set of
parameter values and at least one second set of parameter values,
determining respective matrix quality factors associated with the
first set of parameter values and the at least one second set of
parameter values, comparing the respective matrix quality factors
for determining a preferred set of parameter values, biasing the
matrix with the preferred set of parameter values, and separating
from the biased matrix the desired source signal from the plurality
of source signals.
21. A method according to claim 20 further comprising repeating for
the biased matrix the separating, determining of the error rate and
the comparing thereof, the modifying, determining of the respective
matrix quality factors, the comparing for determining a new
preferred set of parameter values, and biasing of the biased matrix
with the new preferred set of parameter values.
22. A method according to claim 20 wherein the parameters
associated with the matrix are modified so that the respective
matrix quality factors are based upon error rates associated with
the first set of parameter values and the at least one second set
of parameter values.
23. A method according to claim 20 wherein the parameters
associated with the matrix are modified so that the respective
matrix quality factors are based upon constellation clouds
associated with the first set of parameter values and the at least
one second set of parameter values.
24. A method according to claim 20 wherein the parameters
associated with the matrix are modified so that the respective
matrix quality factors are based upon determined lengths of Viterbi
paths associated with the first set of parameter values and the at
least one second set of parameter values.
25. A method according to claim 20 wherein each set of parameter
values associated with the matrix corresponds to a range interval
of solutions of the matrix.
26. A method according to claim 25 wherein at least a portion of
the range intervals of solutions overlap.
27. A method according to claim 20 wherein the linear independent
equations include channel coefficients; and wherein each set of
parameter values associated with the matrix corresponds to a range
interval of the channel coefficients.
28. A method according to claim 20 wherein creating the matrix
includes determining a power level of the different summations of
source signals; wherein involves adjusting relationships between
entries; and wherein each set of parameter values associated with
the matrix corresponds to a range interval of the power levels.
29. A method according to claim 20 wherein separating from the
matrix the desired source signal from the plurality of source
signals is based upon at least one of a Kolmogorov complexity
minimization and a convex optimization.
30. A method according to claim 20 wherein the error rate is
compared to a threshold for determining acceptability.
31. A method according to claim 20 wherein after determining the
error rate and before determining the respective matrix quality
factors; further comprising adding entries to the matrix so that a
number of the unknowns in the matrix is reduced.
32. A method according to claim 31 wherein the entries are added
based upon at least one of adjusting range intervals of the matrix,
adjusting relationships between entries, and adjusting power levels
of the matrix entries.
33. A method according to claim 31 wherein the entries are added
based upon at least one of adjusting range intervals of the matrix,
and adjusting power levels of the matrix.
34. A method according to claim 20 wherein the antenna array
comprises at least one antenna element.
Description
FIELD OF THE INVENTION
The present invention relates to the field of signal processing,
and more particularly, to separating desired source signals from a
mixture of source signals in which rank deficient matrices are
formed.
BACKGROUND OF THE INVENTION
In communications networks there are source signals intended for a
specific communications device, and there are source signals
intended for other communications devices operating within the same
frequency band. There are also sources of noise which produce
signals that are not used for communications, but are received by
the communications devices as well.
To facilitate decoding of the source signals of interest, signal
separation is used to separate the signals received by a
communications device. If the signals can be separated without any
knowledge about the nature of the signals or the transformations
that occur due to interactions between the signals and the
communication channel, then this is known as blind signal
separation In practical implementations, any knowledge that is
available is often exploited In this case, the signal separation is
semi-blind or non-blind. When the processing is non-blind, signal
extraction techniques are often used instead of separation The
difference being that more of the interferers are treated as noise
than in the separation procedures
In blind signal separation techniques, the received signals are
often compactly represented by matrix equations of the form: x=As+n
Equation 1 where x is the received signal vector, A is the mixing
matrix, s is the received vector composed of desired and undesired
signals which are separable by signal processing, and n is an
aggregate noise vector composed of random noise sources and any
actual signal not included in the s vector
The mixing matrix A and signals remain combined in the received
signal vector s such that y=W(As)+Wn=Wx Equation 2 where W is the
separation matrix, and y is a vector that is a subset of s in an
unknown order with scaling changes. If all the signals are not
separable, then the noise term n includes the residual signal due
to the unidentifiable sources.
In semi-blind or non-blind signal separation techniques, A is
referred to as the channel matrix, and the signal vector s may be
solved by determining the inverse channel matrix:
s'=A.sup.-1x=A.sup.-1(As)+A.sup.-1n=s+A.sup.-1n Equation 3 s' is
therefore the signal vector of interest plus noise multiplied by
the inverse channel matrix. Traditional techniques may be used to
find the inverse of the channel.
For purposes of discussion, the channel matrix and the mixing
matrix will be generally referred to herein simply as the matrix.
Regardless of whether the matrix is a mixing matrix for blind
signal separation or a channel matrix for non-blind/semi-blind
signal separation, the rank of the matrix determines how many
signals can actually be separated. For example, a matrix having a
rank of 4 means that 4 source signals can be separated. Ideally,
the rank of the matrix should at least be equal to the number of
signal sources. The larger the rank, the more signals that can be
separated.
If there is an equal number of linear equations in the matrix as
there are unknowns, then the matrix is said to be rank sufficient.
To solve a rank sufficient matrix, an L0-norm technique can be used
to provide the unique solution. This is the ideal case in which the
matrix is adequately populated so that the number of unknown
variables is equal to the number of linear equations.
However, when the matrix contains more unknown variables than
linear equations, the matrix is underdetermined. In an
underdetermined matrix, various combinations of the variables may
be utilized to satisfy the matrix constraints. In this situation,
there are infinitely many solutions,
One approach to solving a rank deficient matrix is to increase the
rank of the matrix. U.S. published patent application No.
2006/0066481 discloses several such techniques for increasing the
rank of the matrix. This patent is assigned to the current assignee
of the present invention, and is incorporated herein by reference
in its entirety. To increase the rank of the matrix associated with
a communications device, more antennas may be added to populate the
matrix with additional linearly independent signal sums. However,
small portable communications devices have little available volume
for a large number of antennas, and mounting the antennas on the
outside of the communications devices is a problem for the
users.
Consequently, there is a need to separate signals from an
underdetermined matrix without increasing the number of antennas.
Research by David Donoho of Stanford University concludes that for
most underdetermined systems of equations, when a sufficiently
sparse solution exits, it can be found by convex optimization. More
precisely, for a given ratio of unknowns (m) to equations (n),
there is a threshold p so that most large n by m matrices generate
systems of equations with two properties: 1) if convex optimization
is run to find an L1-norm minimal solution, and the solution has
fewer than pn non-zeros, then this is the unique sparsest solution
to the equations, and 2) if the result does not have pn non-zeros,
there is no solution with <pn non-zeros.
Donoho has shown that under specific conditions rank deficient
matrices can be uniquely solved. However, a problem remains that
while the number of solutions may be reduced to a finite number or
at least a more constrained set, a unique solution may still not be
obtained.
SUMMARY OF THE INVENTION
In view of the foregoing background, it is therefore an object of
the present invention to obtain a unique solution to rank deficient
matrices if a unique solution is not initially obtained.
This and other objects, features, and advantages in accordance with
the present invention are provided by a communications device
comprising an antenna array for receiving different summations of
source signals from a plurality of signal sources, and a receiver
coupled to the antenna array for receiving the different summations
of source signals. A signal separation processor is coupled to the
receiver.
The signal separation processor performs the following. A matrix
based upon the different summations of source signals is created,
with the matrix being defined by linear independent equations with
fewer equations than unknowns. In other words, the matrix is
underdetermined.
The signal separation processor separates from the matrix a desired
source signal from the plurality of source signals, determines an
error rate associated with the desired source signal, and compares
the error rate to a threshold. Separating from the matrix the
desired source signal from the plurality of source signals may be
based upon a convex optimization. If the error rate is not
acceptable based upon the comparing, then parameters associated
with the matrix are modified based upon a first set of parameter
values and based upon at least one second set of parameter
values
The signal separation processor also determines respective matrix
quality factors associated with the first set of parameter values
and with the at least one second set of parameter values, and
compares the respective matrix quality factors for determining a
preferred set of parameter values. The matrix is biased with the
preferred set of parameter values.
The signal separation processor also separates from the biased
matrix the desired source signal from the plurality of source
signals In addition, the above steps may be repeated so that the
biased matrix is biased with a new preferred set of parameters. As
a result, if the rank deficient processing initially performed on
the matrix was not able to determine a unique solution, then
parameters associated with the matrix are modified based upon
different sets of parameter values, and respective matrix quality
factors associated with the different sets of parameter values are
determined. The matrix is then biased with the preferred set of
parameter values so that the solution space may be narrowed for
obtaining a solution.
In one approach for narrowing the solution space, the parameters
associated with the matrix are modified so that the respective
matrix quality factors are based upon error rates associated with
the first set of parameter values and the at least one second set
of parameter values.
In another approach for narrowing the solution space, the
parameters associated with the matrix are modified so that the
respective matrix quality factors are based upon constellation
clouds associated with the first set of parameter values and the at
least one second set of parameter values.
In yet another approach for narrowing the solution space, the
parameters associated with the matrix are modified so that the
respective matrix quality factors are based upon determined lengths
of Viterbi paths associated with the first set of parameter values
and the at least one second set of parameter values.
Each set of parameter values associated with the matrix may
correspond to a range interval of solutions of the matrix. At least
a portion of the range intervals of solutions may overlap. The
linear independent equations include channel coefficients, and each
set of parameter values associated with the matrix may correspond
to a range interval of the channel coefficients. Moreover, creating
the matrix may also include determining a power level of the
different summations of source signals, wherein each set of
parameter values associated with the matrix may correspond to a
range interval of the power levels. Moreover, creating the matrix
may also include placing restrictions on the relative values
between the entries of the signal solutions vector.
Yet another option for narrowing the solution space is to increase
the rank of the matrix. The processor may be configured so that
after determining the error rate and before determining the
respective matrix quality factors, entries are added to the matrix
so that a number of the unknowns in the matrix is reduced,
restricted in range in regards to a fixed value or values, or in
relationship to other variables. The added entries may be based
upon at least one of adjusting range intervals of the matrix, and
adjusting power levels of the matrix.
The antenna array comprises at least one antenna element. The at
least one antenna element may comprise a plurality of active
antenna elements so that the antenna array forms a phased array.
Alternately, the at least one antenna element comprises a plurality
of active antenna elements so that the antenna array forms a
switched beam antenna. Alternately, the at least one antenna
element comprises a plurality of active antenna elements subject to
a change of characteristic impedance by either loading elements or
ground planes.
Another aspect of the present invention is directed to a method for
operating a communications as defined above.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a typical operating scenario in which
a communications device receives desired and undesired signals from
their respective signal sources in accordance with the present
invention.
FIG. 2 is a more detailed block diagram of the communications
device shown in FIG. 1.
FIG. 3 is a generic flow chart for processing a rank deficient
matrix in accordance with the present invention.
FIG. 4 is a more detailed flow chart for processing a rank
deficient matrix based upon error rates in accordance with the
present invention,
FIG. 5 is a more detailed flow chart for processing a rank
deficient matrix based upon constellation tightness in accordance
with the present invention.
FIG. 6 is a plot of different constellation points based upon
different matrix parameters in accordance with the present
invention.
FIG. 7 is a more detailed flow chart for processing a rank
deficient matrix based upon Viterbi path lengths in accordance with
the present invention.
FIG. 8 is a diagram of a Viterbi trellis and a trace back there
through in accordance with the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention will now be described more fully hereinafter
with reference to the accompanying drawings, in which preferred
embodiments of the invention are shown. This invention may,
however, be embodied in many different forms and should not be
construed as limited to the embodiments set forth herein. Rather,
these embodiments are provided so that this disclosure will be
thorough and complete, and will fully convey the scope of the
invention to those skilled in the art. Like numbers refer to like
elements throughout, and prime, double prime and triple prime
notations are used to indicate similar elements in alternative
embodiments.
In communications networks there are source signals intended for a
specific communications device, and there are source signals
intended for other communications devices operating within the same
frequency band. There are also sources of noise which produce
signals that are not used for communications, but are received by
the communications devices as well. To facilitate decoding of the
source signals of interest, various signal separation techniques
are used.
A typical scenario is illustrated in FIG. 1, in which a plurality
of signal sources 20 transmit source signals 22. The source signals
22 are transmitted in a direction based upon generated antenna
beams 24 associated with each respective signal source 20, The
plurality of signal sources 20 include a first signal source 20(1)
through an Mth signal source 20(M). Likewise, the respective source
signals are referenced 22(1)-22(M) and the corresponding antenna
beams are referenced 24(1)-24(M). More straightforward
implementations are often utilized in communications networks in
the form of omni-directional antenna patterns or directional
antenna patterns.
The communications device 30 jointly extracts the mixture of source
signals received by the antenna array 32 by sampling an aggregate
or composite of the received source signals. The output of each
antenna element 34 is modeled as a summation of the source signals
22 after having been convolved with the impulse response of the
channel, i.e., the propagation path between the output of a signal
source 20 and the output of an antenna element 34 plus additive
Gaussian noise.
The antenna array 32 thus receives a linear combination or mixture
of the source signals 22 from the signal sources 20. The
illustrated antenna array 32 comprises a plurality of antenna
elements 34, with each antenna element providing at least one
linear combination or mixture of the source signals 22 from the
signal sources 20. The antenna elements 34 include a first antenna
element 34(1) through an Nth antenna element 34(N). However, even
though the antenna array 32 is illustrated with a plurality of
antenna elements 34(1)-34(N), the array may comprise only a single
antenna element for receiving the linear combination or mixture of
the source signals 22 from the signal sources 20.
The received source signals 22(1)-22(M) are initially formed into a
matrix 36 for processing by signal separation processing module 38.
If the matrix is rank sufficient, that is, it has a unique
solution, then the communications device 30 uses either blind
signal separation techniques or non-blind/semi-blind signal
separation techniques for separating the source signals in the
matrix 36. The separated signals are represented by reference
39.
However, if the matrix 36 is rank deficient, then there is no
unique solution. The matrix 36 is rank deficient when the linear
independent equations are less then the unknowns. In this case,
there are infinitely many solutions for the signal separation
processing module 38 to choose from As discussed above, Donoho
concludes that for most underdetermined systems of equations, when
a sufficiently sparse matrix exits, it can be found by convex
optimization. The separated signals are also represented by
reference 39.
The communications device 30 for separating source signals provided
by the M signal sources 20(1)-20(M) will now be discussed in
greater detail with reference to FIG. 2, and with an emphasis being
placed on separating signals when the matrix 36 is rank deficient.
The antenna array 32 is not limited to any particular
configuration, and may include one or more antenna elements
34(1)-34(N) as noted above. When there is more than one antenna
element 34(1)-34(N), they may be configured so that the antenna
array 32 forms a phased array or switched beam antenna, for
example. A transceiver 40 is connected downstream to the antenna
array 32 for receiving up to the at least N different summations of
the M source signals 22.
As an alternative to the phased array antenna or switched beam
antenna changing the antenna patterns, a ground plane or loading
elements may also be utilized via changes in characteristic
impedance to deform the antenna array patterns. More particularly,
the antenna array may comprise a ground plane adjacent the at least
one antenna element, and the at least one antenna element may
comprise an active antenna element, and at least one passive
antenna elements. The passive antenna element comprises an upper
half and a corresponding lower half, and a variable reactive load
connecting the upper half to the ground plane for changing the
antenna pattern. Alternatively, the ground plane is adjacent the at
least one antenna element, and a controller is coupled to the
ground plane for changing an antenna pattern. The controller
includes an RF choke, for example. These two alternatives are
discussed in greater detail in the above referenced patent
application assigned to the current assignee of the present
invention.
A processor 42 is downstream to the transceiver 40. Even though the
processor 42 is illustrated separate form the transceiver 40, the
processor may also be included within the transceiver. Even though
the mixing matrix 36 and the separated signals 39 were shown
separate from the signal separation processing module 38, they may
also be included within the module as shown in FIG. 2.
The different summations of the M source signals 22 received by the
transceiver 40 are used to populate the matrix 36, which in this
case is underdetermined. The underdetermined matrix 36 is then
processed by a rank deficient processing module 44 using convex
optimization for example, and if a solution to the matrix cannot be
determined, the solution space narrowing processing module 46
processes the matrix 36 in order to narrow the solution space for
determining a solution to the matrix.
The solution space narrowing processing module 46 selects subsets
of solution space values of the matrix 36 so that the matrix can be
biased with one of the subsets for obtaining a solution for data
processing. As will be discussed in greater detail below, the
solution space for the matrix 36 may be narrowed based upon error
rates, constellation tightness and Viterbi path lengths.
Once the signals are separated, they undergo signal analysis by a
signal analysis module 50 to determine which signals are of
interest and which signals are interferers. An application
dependent processing module 52 processes the signals output from
the signal analysis module 50.
The decision on which signals are of interest may not always
involve the final signal to be decoded. For instance, the
application may call for identifying interferers and subtracting
them from the different summations of the received source signals,
and then feeding the reduced signal to a waveform decoder. In this
case, the signals of interest are the ones that ultimately end up
being rejected
Donoho discloses in two separate but related papers that rank
deficient matrixes can be solved using convex optimization, or
Kolmogorov complexity minimization. The first paper is titled "For
Most Large Undetermined Systems of Linear Equations The Minimal
l.sup.1-norm Is Also The Sparest Solution", dated Sep. 16, 2004,
and the second paper is titled "The Simplest Solution To An
Undetermined System Of Linear Equations" dated Jul. 9-14, 2006.
Both of these papers are incorporated herein by reference in their
entirety The separated signals are also represented by reference
39.
Even though Donoho has shown that under specific conditions rank
deficient matrices can be uniquely solved, a problem remains that
while the number of solutions may be reduced to a finite number or
smaller range set, a unique solution may still not be obtained The
present invention narrows the solution space via the solution space
narrowing processing module 46 when the Donoho method (or some
other rank deficient processing method) is not able to separate the
signals in a rank deficient matrix
Processing of the underdetermined matrix 36 for narrowing the
solution space by generic means will initially be discussed with
reference to the flow chart in FIG. 3. This particular flow chart
provides a generic overview of how the solution space for an
underdetermined matrix 36 is narrowed when an error rate of the
separated signals using convex optimization is not acceptable based
upon convex optimization.
First, the antenna array 32 receives different summations of the
source signals 22(1)-22(M) from the plurality of signal sources
20(1)-20(M). The transceiver 40 is coupled to the antenna array for
receiving the different summations of the source signals
20(1)-20(M). The signal separation processor module 38 is coupled
to the receiver 40 for creating the matrix 36 in Block 70 based
upon the different summations of the source signals 20(1)-20(M),
wherein the matrix is defined by linear independent equations with
fewer equations than unknowns, i.e., underdetermined. The matrix 36
will be either a channel matrix or a mixing matrix.
A decision is made in Block 72 to confirm if the rank of the matrix
36 is sufficient. If the matrix 36 does have a sufficient rank,
i.e., the equations equal the unknowns, then traditional signal
separation techniques are applied in Block 74 for separating the
desired source signals from the plurality of source signals
22(1)-22(M).
Traditional signal separation techniques for rank sufficient
matrices include principal component analysis (PCA), independent
component analysis (ICA) and singular value decomposition (SVD).
PCA involves first and second moment statistics of the source
signals, and is used when the signal-to-noise ratios of the source
signals are high. Otherwise, ICA is used which involves PCA
processing followed by third and fourth moment statistics of the
source signals As an alternative, SVD may be used to separate a
source signal from the mixture of source signals based upon their
eigenvalues. When the matrix is of the channel type, some
traditional signal extraction techniques are minimum mean square
estimation, zero forcing, and matched filtering.
If the matrix 36 does not have a sufficient rank, then rank
deficient processing is applied to the matrix in Block 76. The rank
deficient processing uses convex optimization for example, to
separate the desired source signals from the undesired source
signals as discussed above.
A portion of the separated desired source signal is decoded to
determine an error rate associated therewith in Block 78. This
error is compared to a threshold in Block 80. If the error rate is
below an acceptable threshold, then the desired separated source
signal is passed to Block 82 for decoding and data processing. If
the error rate of the desired separated source signals is not
acceptable, then processing continues to Block 84.
In Block 84, a determination is made if additional boundary
constraints are available. If yes, then the constraints are added
to the matrix 36 in Block 86, and the process loops back to Block
76. Adding additional range boundary constraints adds new entries
into the matrix 36. Any entry or value in the matrix 36 may be
changed, which in turns adds constraints to the matrix. For
example, restrictions on the values in the matrix 36 may be greater
than 0. Also, a range limit may be placed on certain values in the
matrix 36, such as the power levels of the signals of interest are
to be less than 0.5 watts, for example. Certain channel
coefficients within the matrix 36 may also be modified.
As a result of anyone of a number of possible constraints, the rank
of the matrix 36 is increased. If the rank is increased so that the
error rate of the separated signals in Blocks 78 and 80 are below
the acceptable threshold, then the process proceeds to Block 82 for
decoding and data analysis.
If no additional constraints are available, then the parameters
associated with the matrix 36 are modified based upon a first set
of parameter values and at least one second set of parameter
values. The first set of parameters is selected in Block 90, which
is a subset M1 of the solution space for the matrix 36, which is
also represented by the reference M in the flow chart. The at least
one second set of parameter values is selected in Block 92, which
is also a subset M2 of the solution space for M. The at least one
second set could be one or more test areas even though the
flowchart only shows a single second solution space M2. The subsets
may be separate or they may overlap one another.
Based upon the first and second subset of values M1 and M2,
respective matrix quality factors associated with the first set of
parameter values and the at least one second set of parameter
values are determined in Blocks 94 and 96. If the two quality
factors are not significantly different as determined in Block 98,
then the process proceeds to the decoding and data processing Block
83. If the determined quality values are significantly different
from one another, then the subset of values corresponding to the
better quality factor is used to bias the matrix in Block 102 or
104.
The biased matrix is then run through the rank deficient processing
Block 76. The steps in Blocks 78-104 are repeated through an
iterative cycle until the two different quality factors in Blocks
94, 96 are not significantly different from one another in Block
98. When this occurs, the process now continues to the decoding and
data processing Block 82
FIG. 4 is similar to FIG. 3, but is directed to narrowing the
solution space due to error rates. Blocks 94'-104' are similar to
the generic Blocks 94-104 in FIG. 3, but are directed to the
quality factor being associated with error rates. In particular,
the parameters in Blocks 90, 92 associated with the matrix are
modified so that the respective matrix quality factors in Blocks
94', 96' are based upon error rates associated with the first set
of parameter values and the at least one second set of parameter
values. The matrix 36 is biased based upon the parameters providing
the lowest error rate,
FIG. 5 is similar to FIG. 3, but is directed to narrowing the
solution space due to constellation tightness. Blocks 94''-104''
are similar to the generic Blocks 94-104 in FIG. 3, but are
directed to the quality factor being associated with constellation
points. In particular, the parameters in Blocks 90, 92 associated
with the matrix are modified so that the respective matrix quality
factors in Blocks 94'', 96'' are based upon a constellation
tightness associated with the first set of parameter values and the
at least one second set of parameter values. The matrix 36 is
biased based upon the parameters providing the tightest grouping of
constellation points.
For a better illustration of constellation points, reference is
directed to FIG. 6. The ideal position of four modulation
constellation points is provided in plot 120. The tightness of the
first set of parameters associated with the constellation points in
Block 90 is provided in plot 122. Similarly, the tightness of the
second set of parameters associated with the constellation points
in Block 92 is provided in plot 124. As shown, the second parameter
set in Block 92 is more tightly distributed around the
constellation points than the first set of parameters in Block 90.
The second set of parameters is selected in Block 100''. One means
for determining this mathematically is by determining the average
distance between the points in each quadrant.
FIG. 7 is similar to FIG. 3, but is directed to narrowing the
solution space due to Viterbi path lengths. Blocks 94'''-104''' are
similar to the generic Blocks 94-104 in FIG. 3, but are directed to
the quality factor being associated with Viterbi path lengths. In
particular, the parameters in Blocks 90, 92 associated with the
matrix are modified so that the respective matrix quality factors
in Blocks 94''', 96''' are based upon Viterbi path lengths
associated with the first set of parameter values and the at least
one second set of parameter values. The matrix 36 is biased based
upon the parameters providing the shortest Viterbi path length.
For a better illustration of Viterbi path lengths, reference is
directed to FIG. 8. The Viterbi trellis 130 illustrates several
trace backs between the various states. The M parameters which
produce the shortest path through the trellis would be picked for
the next iteration of the rank deficient processing in Block 76. At
t=5 for example, the path 132 through the trellis 130 corresponding
to the actual message is still associated with the smallest
accumulated error metric. This is exploited by the Viterbi decoder
to recover the original message.
Many modifications and other embodiments of the invention will come
to the mind of one skilled in the art having the benefit of the
teachings presented in the foregoing descriptions and the
associated drawings. Therefore, it is understood that the invention
is not to be limited to the specific embodiments disclosed, and
that modifications and embodiments are intended to be included
within the scope of the appended claims.
* * * * *